{
  "abstract": "Let k be an integer from 1 to n, let f be a positive smooth function on the unit sphere, and consider the normalized flow X_t = -f({nu})|X|^{alpha} sigma_k({kappa}) {nu} + beta X, beta = C_n^k. In the supercritical range alpha > k+1, we prove the flow exists for all time and converges exponentially in C^{infty}, from every smooth strictly convex initial hypersurface enclosing the origin, to the unique smooth strictly convex solution of f(x)r^{alpha} sigma_k({kappa}) = beta u. The convergence is driven by the relative residual p = (log u)_t = beta - f(x)r^{alpha} {sigma}_k({kappa})/u, whose L^{infty} norm is nonincreasing and decays with the explicit exponent beta(alpha-k-1); the residual estimates are proved before, and independently of, the curvature estimates. Existence of a strictly convex solution of the stationary equation in this range, for arbitrary positive angular data, was previously obtained by Bryan-Ivaki-Scheuer through an expanding-type flow started from a barrier; the contribution here is the convergence of the normalized contracting flow from arbitrary initial data, with an explicit exponential rate, together with uniqueness of the limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35241",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongyi Sheng"
    },
    {
      "name": "Weimin Sheng"
    },
    {
      "name": "Jiazhuo Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3w3fnmgxv9cfg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35241",
  "fulltext_url": null,
  "id": "3w3fnmgxv9cfg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35241",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.DG"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7214740340",
  "pdf_url": "https://arxiv.org/pdf/2609.35241",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3w3fnmgxv9cfg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35241",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35241"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Supercritical dual k-Minkowski flows with general prescribed data: a priori estimates and asymptotic convergence",
  "title_text": "Supercritical dual k-Minkowski flows with general prescribed data: a priori estimates and asymptotic convergence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/3w3fnmgxv9cfg",
  "venue": "arXiv",
  "versions": []
}